We present soft ( 0.5-2 keV ) X-ray luminosity functions ( XLFs ) in the Great Observatories Origins Deep Survey ( GOODS ) fields , derived for galaxies at z \sim 0.25 and 0.75 .
SED fitting was used to estimate photometric redshifts and separate galaxy types , resulting in a sample of 40 early-type galaxies and 46 late-type galaxies .
We estimate k-corrections for both the X-ray/optical and X-ray/NIR flux ratios , which facilitates the separation of AGN from the normal/starburst galaxies .
We fit the XLFs with a power-law model using both traditional and Markov-Chain Monte Carlo ( MCMC ) procedures .
A key advantage of the MCMC approach is that it explicitly takes into account upper-limits and allows errors on “ derived ” quantities such as luminosity densities to be computed directly ( i.e. , without potentially questionable assumptions concerning the propagation of errors ) .
The slopes of the early-type galaxy XLFs tend to be slightly flatter than the late-type galaxy XLFs although the effect is significant at only the 90 % and 97 % levels for z \sim 0.25 and 0.75 .
The XLFs differ between z < 0.5 and z > 0.5 , at > 99 \% significance levels for early-type , late-type and all ( early and late-type ) galaxies .
We also fit Schechter and log-normal models to the XLFs , fitting the low and high redshift XLFs for a given sample simultaneously assuming only pure luminosity evolution .
In the case of log-normal fits , the results of MCMC fitting of the local FIR luminosity function were used as priors for the faint and bright-end slopes ( similar to “ fixing ” these parameters at the FIR values except here the FIR uncertainty is included ) .
The best-fit values of the change in \log L ^ { * } with redshift were \Delta \log L ^ { * } = 0.23 \pm 0.16 dex ( for early-type galaxies ) and 0.34 \pm 0.12 dex ( for late-type galaxies ) , corresponding to ( 1 + z ) ^ { 1.6 } and ( 1 + z ) ^ { 2.3 } .
These results were insensitive to whether the Schechter or log-normal function was adopted .